4x-(3x-7)-(2x-3)=8x(x-1)

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Solution for 4x-(3x-7)-(2x-3)=8x(x-1) equation:


Simplifying
4x + -1(3x + -7) + -1(2x + -3) = 8x(x + -1)

Reorder the terms:
4x + -1(-7 + 3x) + -1(2x + -3) = 8x(x + -1)
4x + (-7 * -1 + 3x * -1) + -1(2x + -3) = 8x(x + -1)
4x + (7 + -3x) + -1(2x + -3) = 8x(x + -1)

Reorder the terms:
4x + 7 + -3x + -1(-3 + 2x) = 8x(x + -1)
4x + 7 + -3x + (-3 * -1 + 2x * -1) = 8x(x + -1)
4x + 7 + -3x + (3 + -2x) = 8x(x + -1)

Reorder the terms:
7 + 3 + 4x + -3x + -2x = 8x(x + -1)

Combine like terms: 7 + 3 = 10
10 + 4x + -3x + -2x = 8x(x + -1)

Combine like terms: 4x + -3x = 1x
10 + 1x + -2x = 8x(x + -1)

Combine like terms: 1x + -2x = -1x
10 + -1x = 8x(x + -1)

Reorder the terms:
10 + -1x = 8x(-1 + x)
10 + -1x = (-1 * 8x + x * 8x)
10 + -1x = (-8x + 8x2)

Solving
10 + -1x = -8x + 8x2

Solving for variable 'x'.

Combine like terms: -1x + 8x = 7x
10 + 7x + -8x2 = -8x + 8x2 + 8x + -8x2

Reorder the terms:
10 + 7x + -8x2 = -8x + 8x + 8x2 + -8x2

Combine like terms: -8x + 8x = 0
10 + 7x + -8x2 = 0 + 8x2 + -8x2
10 + 7x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
10 + 7x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1.25 + -0.875x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -0.875x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -0.875x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -0.875x + x2 = 0 + 1.25
-0.875x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-0.875x + x2 = 1.25

The x term is -0.875x.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875x + 0.19140625 + x2 = 1.25 + 0.19140625

Reorder the terms:
0.19140625 + -0.875x + x2 = 1.25 + 0.19140625

Combine like terms: 1.25 + 0.19140625 = 1.44140625
0.19140625 + -0.875x + x2 = 1.44140625

Factor a perfect square on the left side:
(x + -0.4375)(x + -0.4375) = 1.44140625

Calculate the square root of the right side: 1.200585795

Break this problem into two subproblems by setting 
(x + -0.4375) equal to 1.200585795 and -1.200585795.

Subproblem 1

x + -0.4375 = 1.200585795 Simplifying x + -0.4375 = 1.200585795 Reorder the terms: -0.4375 + x = 1.200585795 Solving -0.4375 + x = 1.200585795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 1.200585795 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 1.200585795 + 0.4375 x = 1.200585795 + 0.4375 Combine like terms: 1.200585795 + 0.4375 = 1.638085795 x = 1.638085795 Simplifying x = 1.638085795

Subproblem 2

x + -0.4375 = -1.200585795 Simplifying x + -0.4375 = -1.200585795 Reorder the terms: -0.4375 + x = -1.200585795 Solving -0.4375 + x = -1.200585795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -1.200585795 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -1.200585795 + 0.4375 x = -1.200585795 + 0.4375 Combine like terms: -1.200585795 + 0.4375 = -0.763085795 x = -0.763085795 Simplifying x = -0.763085795

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.638085795, -0.763085795}

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